integrate function (x^4+3x)/(x^2) with respect to x

split the integral into (x^4)/(x^2) and (3x)/(x^2) which becomes x^2 and 3*(1/x). These can now be integrated separately and added together after the integration.

first integral: raise the power form 2 to 3, then divide by the new power. This gets (x^3)/3

second integral: remove the 3 from within the integral. realise that 1 is the differential of x. Thereofore 1/x satisfies the condition of f'(x)/f(x). When a function like this is integrated, the answer becomes logarithmic Becoming ln(f(x)) which is ln(x)

therefore the final answer is (x^3)/3+3*ln(x)